ROSE TREE MEDIA SCHOOL DISTRICT
COURSE CURRICULUM
COURSE TITLE: Algebra II, Level 1
GRADE LEVEL: High School
CREATION DATE: November 2003
Essential Question, Concept or Theme: A. Equations and Inequalities
PA Standards: 2.1.11.A,2.2.11.A, 2.2.11.B, 2.5.11.A-C, 2.8.11.A
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
Benchmark 1: Students will use the order
of operations to evaluate expressions.
Skill Set
Correctly implement the hierarchy of
PEMDAS
Define and apply the following vocabulary:
parentheses, braces, brackets, and algebraic
expression
Tests, quizzes, and a
cumulative final exam.
Covered on a Midterm exam.
Benchmark 2: Students will use formulas
for problem solving.
Skill Set
Define and apply the following vocabulary:
formula, algebraic expression, Pythagorean
theorem, hypotenuse, legs.
Approx. Time Allotment:
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment, performance
assessment, group activities,
or board work.
Benchmark 3: Students will determine
the sets of numbers to which a given
number belongs.
Skill Set
State a definition for the number sets
including real (R), rational (Q), irrational
(I), whole (W), integer (Z), and/or natural
number (N)
Use a Venn diagram to illustrate the
relationship between the sets of numbers.
Algebra II - Integration,
Applications & Connections Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and
overhead view screen.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software applications
for classroom demonstration or
individual student exploration.
Internet links suggested in the
text.
Videos available in the
Penncrest Math Office.
Boxer Math
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work independently of
the instructor and are permitted to
work with other students.
Optional instructional strategies
may include:
Group work, or any variety of
classroom activities such as “List,
Pass, Amass”, “Each one, teach
one”, etc. as suggested by the
Professional Development
Coordinator.
Independent investigations
Boxer Math Applications
Benchmark 4: Students will use
properties of real numbers to simplify
expressions.
Algebra II, Level 1
Page 1
-1-
November 2003
Essential Question, Concept or Theme: A. Equations and Inequalities
PA Standards: 2.1.11.A,2.2.11.A, 2.2.11.B, 2.5.11.A-C, 2.8.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Skill set
Use the commutative property, associative
property, identity property, inverse property,
and/or distributive property to simplify an
expression or equation.
Benchmark 5: Students will translate
verbal expressions and sentences into
algebraic expressions and equations.
Skill set
Define and apply the following vocabulary:
variable, open sentence, equation, and
inequality
Benchmark 6: Students will solve
equations for a specific variable using the
properties of equality.
Skill set
Students will apply the reflexive,
symmetric, transitive, substitution,
addition/subtraction, and
multiplication/division properties of equality
to determine the solution set of an equation.
Benchmark 7: Students will use a
graphing calculator to estimate solutions
of equations by building tables of values.
Skill set
Demonstration basic understanding of the
use of the TI-82, 83, or 83-plus graphing
calculator.
Algebra II, Level 1
Page 2
-2-
November 2003
Essential Question, Concept or Theme: A. Equations and Inequalities
PA Standards: 2.1.11.A,2.2.11.A, 2.2.11.B, 2.5.11.A-C, 2.8.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 8: Solve problems containing
absolute value and/or inequalities.
Skill set
Solve an inequality using the
addition/subtraction and
multiplication/division properties of
inequality
Solve compound inequalities using “and”
and “or” and relate “and” to “intersection”
and relate “or” to “union”.
Solve inequalities involving absolute value
and graph the solution set.
Algebra II, Level 1
Page 3
-3-
November 2003
Essential Question, Concept or Theme: A. Equations and Inequalities
PA Standards: 2.1.11.A,2.2.11.A, 2.2.11.B, 2.5.11.A-C, 2.8.11.A
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special
instructional needs will be met in accordance
with each student’s Individualized Educational
Plan.
By definition as a level 1 course,
this course is an enrichment course.
Students will be asked to perform
more difficult tests, quizzes, and
homework assignments than those
in the level 2 or 3 versions of this
course. In addition, the students
will complete two units in an
independent study format.
Due to the accelerated nature
of this course, any student
needing serious and ongoing
remediation will be advised
to consider being reassigned
to the level 2 Algebra II
course. Otherwise, students
will be advised to stay after
school for extra help, utilize
the Mu Alpha Theta tutoring
service offered at Penncrest,
or seek professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Use enrichment workbook
associated with current textbook to
cover many optional topics such as
4X4 determinants, probability
topics, etc.
Algebra II, Level 1
Page 4
-4-
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the
math topics to other fields of
study. Likewise, many of the
applications involve examples
that are multicultural in nature.
November 2003
Essential Question, Concept or Theme: B. Linear Relations and Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.D, 2.8.11.K, 2.8.11.L,N, 2.8.11.O,P,Q,T
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark 1: Students will graph a
relation, state its domain and range
and determine if it is a function.
Skill set
Define and apply the following
vocabulary: ordered pairs, coordinate
system, Cartesian coordinate plane, xaxis, y-axis, origin, quadrant, relation,
domain, range, mapping, function,
discrete function, vertical line test,
continuous function
Tests, quizzes, and a cumulative
final exam.
Covered on a Midterm exam.
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom, oral
assessment, performance
assessment, group activities, or
board work.
Benchmark 2: Students will find
values of functions for given elements
of the domain.
Benchmark 3: Students will use
graphing calculator to graph linear
equations.
Skill set
Understand basic use of the TI-82, 83, or
83-plus graphing calculator
Algebra II - Integration,
Applications & Connections
- Glencoe/McGraw-Hill,
1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and
overhead view screen.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software
applications for classroom
demonstration or individual
student exploration.
Internet links suggested in the
text.
Videos available in the
Penncrest Math Office.
Boxer Math
Approx. Time Allotment:
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work independently of
the instructor and are permitted to
work with other students.
Optional instructional strategies
may include:
Group work, or any variety of
classroom activities such as “List,
Pass, Amass”, “Each one, teach
one”, etc. as suggested by the
Professional Development
Coordinator.
Independent investigations
Boxer Math Applications
Benchmark 4: Students will identify
and graph linear equations.
Skill set
Identify the dependent and independent
variable, linear equation, linear function
Write linear equations in standard form
Ax + By = C
Algebra II, Level 1
Page 5
-5-
November 2003
Essential Question, Concept or Theme: B. Linear Relations and Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.D, 2.8.11.K, 2.8.11.L,N, 2.8.11.O,P,Q,T
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Determine the intercepts of a line and
use them to graph an equation.
Approx. Time Allotment:
Instructional Strategies
Determine the x-intercept by setting y =
0, determine the y-intercept by setting x
=0
Determine the slope of a line.
y
Slope = x
Identify from a graph whether the line
has a positive slope, negative slope, zero
slope or undefined slope
Use the slope and a point to graph an
equation.
Locate a point on the graph on a
coordinate plane and use the slope to
identify a second point on the graph
Benchmark 5: Students will
determine whether two lines are
parallel, perpendicular, or neither.
Skill set
Understand that parallel lines have the
same slope, perpendicular lines have
slopes that are negative reciprocals.
Benchmark 6: Students will solve
problems by identifying and using a
pattern.
Benchmark 7: Students will write the
equation of a line.
Algebra II, Level 1
Page 6
-6-
November 2003
Essential Question, Concept or Theme: B. Linear Relations and Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.D, 2.8.11.K, 2.8.11.L,N, 2.8.11.O,P,Q,T
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Skill set
Write an equation of a line in slopeintercept form given the slope and one
or two points.
y  mx  b
Write an equation of a line in pointslope form given two points, or given
the slope and one point.
y  y1  mx  x1 
Write an equation of a line that is
parallel or perpendicular to the graph of
a given equation.
Parallel lines have the same slope;
perpendicular lines have slopes that are
negative reciprocals
Approx. Time Allotment:
Instructional Strategies
Benchmark 8: Students will identify
and graph special functions.
Skill set
Identify and differentiate between direct
variation, constant, identity, step, and/or
absolute value functions.
Benchmark 9: Students will sketch
graphs of inequalities in two
variables.
Skill set
Shade the solution set; use solid or
broken line to form the boundary
depending on the type of inequality.
Algebra II, Level 1
Page 7
-7-
November 2003
Essential Question, Concept or Theme: B. Linear Relations and Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.D, 2.8.11.K, 2.8.11.L,N, 2.8.11.O,P,Q,T
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each student’s
Individualized Educational Plan.
By definition as a level 1
course, this course is an
enrichment course.
Students will be asked to
perform more difficult
tests, quizzes, and
homework assignments
than those in the level 2 or
3 versions of this course.
In addition, the students
will complete two units in
an independent study
format.
Due to the accelerated
nature of this course, any
student needing serious
and ongoing remediation
will be advised to
consider being reassigned
to the level 2 Algebra II
course. Otherwise,
students will be advised
to stay after school for
extra help, utilize the Mu
Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments, preferential
seating, after school help, or modified homework
assignments.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Algebra II, Level 1
Page 8
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
-8-
November 2003
Essential Question, Concept or Theme: C. Systems of Linear Equations and Inequalities
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.D, 2.8.11.F,G,H, 2.8.11.J, 2.8.11.K
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark 1: Students will solve
systems of equations and
inequalities by graphing.
Skill set
Identify the solution set as the point of
intersection or the overlapping region
of the two graphs.
Label systems as consistent or
inconsistent systems, dependent or
independent systems.
Benchmark 2: Students will use the
substitution and elimination
methods to solve systems of
equations.
Benchmark 3: Students will solve
systems of equations by using
Cramer’s rule.
Skill set
Find the values of 2nd order
determinants.
Know and apply Cramer's Rule.
Tests, quizzes, and a cumulative Algebra II - Integration,
final exam.
Applications & Connections Covered on a Midterm exam.
Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
Optional forms of assessment:
graphing calculators and overhead
Homework, projects, teacher
view screen.
observation in the classroom,
oral assessment, performance
Optional Resources:
assessment, group activities, or Teacher resource materials
board work.
associated with the text.
Computer software applications for
classroom demonstration or
individual student exploration.
Internet links suggested in the text.
Videos available in the Penncrest
Math Office.
Boxer Math
Approx. Time Allotment:
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work independently of
the instructor and are permitted to
work with other students.
Optional instructional strategies
may include:
Group work, or any variety of
classroom activities such as “List,
Pass, Amass”, “Each one, teach
one”, etc. as suggested by the
Professional Development
Coordinator.
Independent investigations
Boxer Math Applications
Benchmark 4: Students will solve a
system of three equations in three
variables.
Ordered triple, (x,y,z)
Students will be able to:
Determine the octant in 3Algebra II, Level 1
Page 9
-9-
November 2003
Essential Question, Concept or Theme: C. Systems of Linear Equations and Inequalities
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.D, 2.8.11.F,G,H, 2.8.11.J, 2.8.11.K
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
dimensional space in which a point is
located.
Graph a linear equation in 3
variables and determine the
intercepts.
Find the range, quartiles and inter
quartile range for a set of data.
Determine if any values in a set of
data are outliers.
Represent data using box and
whisker plots.
Algebra II, Level 1
Page 10
Approx. Time Allotment:
Instructional Strategies
- 10 -
November 2003
Essential Question, Concept or Theme: C. Systems of Linear Equations and Inequalities
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.D, 2.8.11.F,G,H, 2.8.11.J, 2.8.11.K
Adaptations/Inclusion Techniques
Adaptations for students with special
instructional needs will be met in accordance
with each student’s Individualized Educational
Plan.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Enrichment Strategies
Remediation Strategies
By definition as a level 1
course, this course is an
enrichment course.
Students will be asked to
perform more difficult
tests, quizzes, and
homework assignments
than those in the level 2 or
3 versions of this course.
In addition, the students
will complete two units in
an independent study
format.
Due to the accelerated nature
of this course, any student
needing serious and ongoing
remediation will be advised
to consider being reassigned
to the level 2 Algebra II
course. Otherwise, students
will be advised to stay after
school for extra help, utilize
the Mu Alpha Theta tutoring
service offered at Penncrest,
or seek professional tutoring
outside of the school day.
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Algebra II, Level 1
Page 11
- 11 -
November 2003
Essential Question, Concept or Theme: D. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.5.11.A-C, 2.8.11.T
Benchmark/Skills
Benchmark 1: Students will
perform basic mathematical
operations with polynomials.
Skill set
Add, subtract, multiply and divide
polynomials.
Define and apply the following
vocabulary: like terms, polynomial,
monomial, binomial, trinomial,
constant, coefficient, degree, power.
Use the rules for multiplying and
dividing exponents
Use the distributive property and
FOIL method
Use the long division and synthetic
division method for dividing
polynomials
Aligned Materials/
Resources/Technology
Assessment
Tests, quizzes, and a cumulative
final exam.
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment, performance
assessment, group activities, or
board work.
Benchmark 2: Students will
perform basic mathematical
operations involving exponents.
Skill set
Represent an expression with a
negative exponent using an
equivalent expression with a positive
exponent.
Represent numbers in scientific
notation.
Multiply and divide exponents
written in scientific notation.
Algebra II, Level 1
Approx. Time Allotment:
Page 12
Algebra II - Integration,
Applications & Connections Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and overhead
view screen.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software applications for
classroom demonstration or
individual student exploration.
Internet links suggested in the text.
Videos available in the Penncrest
Math Office.
Boxer Math
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work independently of
the instructor and are permitted to
work with other students.
Optional instructional strategies
may include:
Group work, or any variety of
classroom activities such as “List,
Pass, Amass”, “Each one, teach
one”, etc. as suggested by the
Professional Development
Coordinator.
Independent investigations
Boxer Math Applications
- 12 -
November 2003
Essential Question, Concept or Theme: D. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.5.11.A-C, 2.8.11.T
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 3: Students will factor
polynomials.
Skill set
Factor polynomials using the
appropriate factoring method: greatest
common factor, perfect square
trinomial, difference of two squares,
sum or difference of two cubes.
Use factoring to simplify polynomial
quotients by factoring and dividing
out common factors.
Benchmark 4: Students will
simplify radicals and radical
expressions.
Skill set
Simplify radicals having various
indices (2nd root, 3rd root, 4th root,
etc.).
Simplify radical expressions.
Rationalize the denominator of a
fraction containing a radical
expression.
Benchmark 5: Students will
perform basic mathematical
operations with radicals.
Skill set
Add, subtract, multiply or divide
radical expressions.
Identify like terms.
Write expressions with rational
Algebra II, Level 1
Page 13
- 13 -
November 2003
Essential Question, Concept or Theme: D. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.5.11.A-C, 2.8.11.T
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
exponents in simplified radical form
and vice versa.
Evaluate expressions in either
exponential or radical form.
Benchmark 6: Students will solve
equations and inequalities
containing radicals.
Skill set
Simplify by squaring both sides of an
equation.
Identify extraneous solutions.
Benchmark 7: Simplify square
roots containing negative
radicands.
Skill set
Rewrite
1 as the number i
Benchmark 8: Solve quadratic
equations that have pure imaginary
solutions.
Skill set
Apply the quadratic formula.
Take the square root of both sides of
an equation.
Benchmark 9: Students will add,
subtract, and multiply complex
Algebra II, Level 1
Page 14
- 14 -
November 2003
Essential Question, Concept or Theme: D. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.5.11.A-C, 2.8.11.T
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
numbers.
Write complex numbers in the form
a + bi
Identify “a” as the real part, and “bi”
as the imaginary part of a complex
number
Use a Venn diagram to illustrate the
relationship between complex, real,
imaginary numbers and all the
subsets of real numbers
Benchmark 10: Simplify
expressions containing complex
numbers in the denominator.
Determine the complex conjugate for
a complex number
Algebra II, Level 1
Page 15
- 15 -
November 2003
Essential Question, Concept or Theme: D. Polynomials and Radical Expressions
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.5.11.A-C, 2.8.11.T
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
By definition as a level 1
course, this course is an
enrichment course.
Students will be asked to
perform more difficult tests,
quizzes, and homework
assignments than those in
the level 2 or 3 versions of
this course. In addition, the
students will complete two
units in an independent
study format.
Due to the accelerated
nature of this course, any
student needing serious and
ongoing remediation will be
advised to consider being
reassigned to the level 2
Algebra II course.
Otherwise, students will be
advised to stay after school
for extra help, utilize the
Mu Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Algebra II, Level 1
Page 16
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 16 -
November 2003
Essential Question, Concept or Theme: E. Quadratic Functions and Inequalities
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.N, 2.8.11.T, 2.11.11.A
Benchmark/Skills
Aligned Materials/
Resources/Technology
Assessment
Tests, quizzes, and a cumulative
final exam.
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment, performance
assessment, group activities, or
board work.
Algebra II, Level 1
Approx. Time Allotment:
Page 17
Algebra II - Integration,
Applications & Connections Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and overhead
view screen.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software applications for
classroom demonstration or
individual student exploration.
Internet links suggested in the text.
Videos available in the Penncrest
Math Office.
Boxer Math
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work independently of
the instructor and are permitted to
work with other students.
Optional instructional strategies
may include:
Group work, or any variety of
classroom activities such as “List,
Pass, Amass”, “Each one, teach
one”, etc. as suggested by the
Professional Development
Coordinator.
Independent investigations
Boxer Math Applications
- 17 -
November 2003
Essential Question, Concept or Theme: E. Quadratic Functions and Inequalities
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.N, 2.8.11.T, 2.11.11.A
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
By definition as a level 1
course, this course is an
enrichment course.
Students will be asked to
perform more difficult tests,
quizzes, and homework
assignments than those in
the level 2 or 3 versions of
this course. In addition, the
students will complete two
units in an independent
study format.
Due to the accelerated
nature of this course, any
student needing serious and
ongoing remediation will be
advised to consider being
reassigned to the level 2
Algebra II course.
Otherwise, students will be
advised to stay after school
for extra help, utilize the
Mu Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Algebra II, Level 1
Page 18
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 18 -
November 2003
Essential Question, Concept or Theme: F. Conic Sections
PA Standards: F.
2.1.11.A, 2.2.11.F,2.5.11.A-C, 2.8.11.E, 2.8.11.T
Benchmark/Skills
Assessment
Benchmark 1: Students will write functions in
quadratic form.
Tests, quizzes, and a
cumulative final exam.
Skill set
Identify quadratic, linear and constant terms
Optional forms of
assessment:
Homework, projects,
teacher observation in the
classroom, oral
assessment, performance
assessment, group
activities, or board work.
Benchmark 2: Students will graph quadratic
functions.
Skill set
Identify the shape of a parabola, the axis of symmetry,
vertex and zeros.
Create a table of values and plot coordinate pairs.
Use symmetry to identify additional points on the
graph.
Benchmark 3: Students will solve quadratic
equations using a variety of methods.
Skill set
Solve quadratic equations by graphing and identify the
zeros as the x-intercepts
Solve quadratic equations by factoring. Use factoring
techniques to include greatest common factor,
difference of two squares, using FOIL “backwards” to
2
2
factor expressions of the form x  bx  c or ax  bx  c
Solve quadratic equations by completing the square.
Solve quadratic equations by using the quadratic
formula.
Use the discriminant to determine the nature of the
roots of a quadratic equation.
Algebra II, Level 1
Page 19
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Algebra II - Integration,
Applications &
Connections Glencoe/McGraw-Hill,
1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and
overhead view screen.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software
applications for classroom
demonstration or individual
student exploration.
Internet links suggested in
the text.
Videos available in the
Penncrest Math Office.
Boxer Math
- 19 -
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work
independently of the
instructor and are permitted to
work with other students.
Optional instructional
strategies may include:
Group work, or any variety of
classroom activities such as
“List, Pass, Amass”, “Each
one, teach one”, etc. as
suggested by the Professional
Development Coordinator.
Independent investigations
Boxer Math Applications
November 2003
Essential Question, Concept or Theme: F. Conic Sections
PA Standards: F.
2.1.11.A, 2.2.11.F,2.5.11.A-C, 2.8.11.E, 2.8.11.T
Benchmark/Skills
Assessment
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Instructional Strategies
Benchmark 4: Students will find the sum and
product of the roots of quadratic equations.
Skill set
Benchmark 5: Students will determine the
quadratic equation that has given roots.
Skill sets
Benchmark 6: Students will graph quadratic
functions and inequalities of the form
Benchmark 7: Students will find the distance
between two points in the coordinate plane.
Benchmark 8: Students will find the midpoint of a
line segment in the coordinate plane.
Benchmark 9: Students will write equations for
2
parabolas using the formula fx  ax  h  k
Benchmark 10: Students will graph parabolas
without the aid of a graphing calculator.
Skill set
Determine the focus, directrix, axis of symmetry, and
latus rectum using appropriate formulas and
relationships based on the equation in standard form.
Algebra II, Level 1
Page 20
- 20 -
November 2003
Essential Question, Concept or Theme: F. Conic Sections
PA Standards: F.
2.1.11.A, 2.2.11.F,2.5.11.A-C, 2.8.11.E, 2.8.11.T
Benchmark/Skills
Assessment
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Instructional Strategies
Optional: Benchmark 11: Students will solve
systems of equations and inequalities involving
quadratics graphically and algebraically.
Skill set
Use combination or substitution methods to determine
the solution set algebraically.
Graph the system of equations with the aid of a
graphing calculator and identify overlapping regions as
the solution set.
Algebra II, Level 1
Page 21
- 21 -
November 2003
Essential Question, Concept or Theme: F. Conic Sections
PA Standards: 2.1.11.A, 2.2.11.F,2.5.11.A-C, 2.8.11.E, 2.8.11.T
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
By definition as a level 1
course, this course is an
enrichment course.
Students will be asked to
perform more difficult tests,
quizzes, and homework
assignments than those in
the level 2 or 3 versions of
this course. In addition, the
students will complete two
units in an independent
study format.
Due to the accelerated
nature of this course, any
student needing serious and
ongoing remediation will be
advised to consider being
reassigned to the level 2
Algebra II course.
Otherwise, students will be
advised to stay after school
for extra help, utilize the
Mu Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Algebra II, Level 1
Page 22
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 22 -
November 2003
Essential Question, Concept or Theme: G. Polynomial Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
Benchmark 1: Students will
evaluate polynomial functions for a
given domain value.
Tests, quizzes, and a cumulative
final exam.
Benchmark 2: Students will
identify general shapes of the
graphs of polynomial functions.
Benchmark 3: Students will find
factors of polynomials.
Skill set
Use the factor theorem and synthetic
division to determine whether a given
polynomial is a factor of another
polynomial.
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment, performance
assessment, group activities, or
board work.
Benchmark 4: Students will
perform a complete analysis of a
simple polynomial function and
sketch the graph of that function.
Skill set
Find the number and type of real
zeros of a polynomial function by
using Descartes' rule of signs.
Use the rational zero theorem to
identify all possible rational zeros of
a polynomial function.
Create a table of values by hand or
with the aid of a graphing calculator
that can be plotted and a curve
sketched.
Algebra II, Level 1
Page 23
Algebra II - Integration,
Applications & Connections Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and overhead
view screen.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software applications for
classroom demonstration or
individual student exploration.
Internet links suggested in the text.
Videos available in the Penncrest
Math Office.
Boxer Math
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work independently of
the instructor and are permitted to
work with other students.
Optional instructional strategies
may include:
Group work, or any variety of
classroom activities such as “List,
Pass, Amass”, “Each one, teach
one”, etc. as suggested by the
Professional Development
Coordinator.
Independent investigations
Boxer Math Applications
- 23 -
November 2003
Essential Question, Concept or Theme: G. Polynomial Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Use the complex conjugates theorem
to identify any additional complex
zero given one complex zero.
Benchmark 5: Students will
perform a complete analysis of a
more complicated polynomial
function with the aid of a graphing
calculator and sketch the graph of
that function.
Skill set
Use the graphing calculator to graph
polynomial functions and to
approximate the real zeros.
Use a graphing calculator to
determine maximum and minimum
values of a function within a specified
range.
Benchmark 6: Students will solve
equations that are quadratic in
form.
Skill set
Apply quadratic techniques to solve
equations for which the degree of the
first term is twice the degree of the
second term, i.e. is quadratic in form.
Benchmark 7: Students will
determine the composition of
functions.
Algebra II, Level 1
Page 24
- 24 -
November 2003
Essential Question, Concept or Theme: G. Polynomial Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 8: Students will
determine and graph the inverse of
a function or relation.
Skill set
Interchange x and y in the equation
and solve for y to find the inverse of a
function, then graph it.
Use the graphing calculator to graph a
function and its inverse.
Reflect the graph of a function across
the line y = x to graph the inverse.
Algebra II, Level 1
Page 25
- 25 -
November 2003
Essential Question, Concept or Theme: G. Polynomial Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
By definition as a level 1
course, this course is an
enrichment course.
Students will be asked to
perform more difficult tests,
quizzes, and homework
assignments than those in
the level 2 or 3 versions of
this course. In addition, the
students will complete two
units in an independent
study format.
Due to the accelerated
nature of this course, any
student needing serious and
ongoing remediation will be
advised to consider being
reassigned to the level 2
Algebra II course.
Otherwise, students will be
advised to stay after school
for extra help, utilize the
Mu Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Algebra II, Level 1
Page 26
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 26 -
November 2003
Essential Question, Concept or Theme: H. Rational Expressions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A 2.11.11.A
Benchmark/Skills
Benchmark 1: Students will graph
rational functions.
Skill set
Determine the asymptotes for a
rational function by examining the
equation and end behavior of the
function.
Determine the values for which the
denominator of a rational function is
undefined.
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Tests, quizzes, and a cumulative
final exam.
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment, performance
assessment, group activities, or
board work.
Benchmark 2: Students will solve
problems involving direct, inverse,
and joint variation.
Benchmark 3: Students will
simplify rational expressions.
Skill set
Apply basic algebraic manipulations
to simplify a rational expression after
factoring the expression
Algebra II - Integration,
Applications & Connections Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and overhead
view screen.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software applications for
classroom demonstration or
individual student exploration.
Internet links suggested in the text.
Videos available in the Penncrest
Math Office.
Boxer Math
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work independently of
the instructor and are permitted to
work with other students.
Optional instructional strategies
may include:
Group work, or any variety of
classroom activities such as “List,
Pass, Amass”, “Each one, teach
one”, etc. as suggested by the
Professional Development
Coordinator.
Independent investigations
Boxer Math Applications
Benchmark 4: Students will
simplify complex fractions.
Skill set
Use the rule of multiplying by the
inverse of the denominator to
simplify complex fractions.
Multiply numerator and denominator
by the common denominator of the
denominators within the complex
fraction.
Algebra II, Level 1
Page 27
- 27 -
November 2003
Essential Question, Concept or Theme: H. Rational Expressions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A 2.11.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 5: Students will add
and subtract rational expressions.
Skill set
Rewrite the expressions with a
common denominator, then add or
subtract
Benchmark 6: Students will solve
rational equations and inequalities.
Skill set
Multiply both sides of the equation by
the least common denominator and
then solve for the variable.
Algebra II, Level 1
Page 28
- 28 -
November 2003
Essential Question, Concept or Theme: H. Rational Expressions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.T, 2.11.11.A 2.11.11.A
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
By definition as a level 1
course, this course is an
enrichment course.
Students will be asked to
perform more difficult tests,
quizzes, and homework
assignments than those in
the level 2 or 3 versions of
this course. In addition, the
students will complete two
units in an independent
study format.
Due to the accelerated
nature of this course, any
student needing serious and
ongoing remediation will be
advised to consider being
reassigned to the level 2
Algebra II course.
Otherwise, students will be
advised to stay after school
for extra help, utilize the
Mu Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Algebra II, Level 1
Page 29
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 29 -
November 2003
Essential Question, Concept or Theme: I. Sequences and Series
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.8.11.C, 2.11.11.D
Benchmark/Skills
Benchmark 1: Students will
determine a specific term in an
arithmetic or geometric sequence, or
geometric series.
Skill set
Define and apply the following
vocabulary: sequence, term, arithmetic
or geometric sequence, common
difference, series sigma, summation
notation.
Determine the nth term of an arithmetic
sequence.
Determine the nth term of a geometric
sequence.
Determine the position of a given term
in an arithmetic or geometric sequence.
Benchmark 2: Students will
determine arithmetic and geometric
means.
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Tests, quizzes, and a cumulative Algebra II - Integration,
final exam.
Applications & Connections Covered on a Midterm exam.
Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
Optional forms of assessment:
graphing calculators and
Homework, projects, teacher
overhead view screen.
observation in the classroom,
oral assessment, performance
Optional Resources:
assessment, group activities, or Teacher resource materials
board work.
associated with the text.
Computer software applications
for classroom demonstration or
individual student exploration.
Internet links suggested in the
text.
Videos available in the Penncrest
Math Office.
Boxer Math
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work independently of
the instructor and are permitted to
work with other students.
Optional instructional strategies
may include:
Group work, or any variety of
classroom activities such as “List,
Pass, Amass”, “Each one, teach
one”, etc. as suggested by the
Professional Development
Coordinator.
Independent investigations
Boxer Math Applications
Benchmark 3: Students will
determine the sum of an arithmetic,
or geometric series.
Determine the sum of an arithmetic
series.
Determine the sum of a geometric series.
Use sigma notation to express sums of
an arithmetic or geometric series.
Determine the sum of an infinite
Algebra II, Level 1
Page 30
- 30 -
November 2003
Essential Question, Concept or Theme: I. Sequences and Series
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.8.11.C, 2.11.11.D
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
geometric series.
Benchmark 4: Students will iterate
functions.
Algebra II, Level 1
Page 31
- 31 -
November 2003
Essential Question, Concept or Theme: I. Sequences and Series
PA Standards: 2.1.11.A, 2.5.11.A-C, 2.8.11.C, 2.11.11.D
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
By definition as a level 1
course, this course is an
enrichment course.
Students will be asked to
perform more difficult tests,
quizzes, and homework
assignments than those in
the level 2 or 3 versions of
this course. In addition, the
students will complete two
units in an independent
study format.
Due to the accelerated
nature of this course, any
student needing serious and
ongoing remediation will be
advised to consider being
reassigned to the level 2
Algebra II course.
Otherwise, students will be
advised to stay after school
for extra help, utilize the
Mu Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Algebra II, Level 1
Page 32
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 32 -
November 2003
Essential Question, Concept or Theme: J. Permutations, Combinations, Probability
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.7.11.A,D,E
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark 1: Students will solve
problems using the Fundamental
Counting Principle.
Skill set
Illustrate fundamental counting principal
problems using a tree diagram
Complete calculations involving
factorials
Identify independent and dependent
events
Solve problems by using the strategy of
solving a simpler problem.
Benchmark 2: Students will solve
problems involving linear and
circular permutations, and
combinations.
Skill set
Differentiate between permutations and
combinations.
Identify conditions that define a
permutation as linear or circular.
Apply formulas to determine
permutations and combinations.
Algebra II, Level 1
Tests, quizzes, and a cumulative Algebra II - Integration,
final exam.
Applications & Connections Glencoe/McGraw-Hill, 1998
Optional forms of assessment:
TI-82, TI-83, or TI-83 Plus
Homework, projects, teacher
graphing calculators and
observation in the classroom,
overhead view screen.
oral assessment, performance
assessment, group activities, or Optional Resources:
board work.
Teacher resource materials
associated with the text.
Computer software applications
for classroom demonstration or
individual student exploration.
Internet links suggested in the
text.
Videos available in the Penncrest
Math Office.
Boxer Math
Page 33
Approx. Time Allotment:
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work independently of
the instructor and are permitted to
work with other students.
Optional instructional strategies
may include:
Group work, or any variety of
classroom activities such as “List,
Pass, Amass”, “Each one, teach
one”, etc. as suggested by the
Professional Development
Coordinator.
Independent investigations
Boxer Math Applications
- 33 -
November 2003
Essential Question, Concept or Theme: J. Permutations, Combinations, Probability
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.7.11.A,D,E
Aligned Materials/
Benchmark/Skills
Assessment
Resources/Technology
Benchmark 3: Students will
determine the probability of an event.
Apply formulas to determine probability
of success or failure.
Approx. Time Allotment:
Instructional Strategies
Find the probability of two or more
independent or dependent events.
Find the probability of mutually
exclusive or inclusive events.
For mutually exclusive events.
For inclusive events.
Benchmark 4: Students will
determine the odds of success and
failure of an event.
Examine the ratio of # of successes to #
of failures to determine the odds of
success or failure
Benchmark 5: Students will
differentiate between probability and
odds.
Algebra II, Level 1
Page 34
- 34 -
November 2003
Essential Question, Concept or Theme: J. Permutations, Combinations, Probability
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.7.11.A,D,E
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
By definition as a level 1
course, this course is an
enrichment course.
Students will be asked to
perform more difficult tests,
quizzes, and homework
assignments than those in
the level 2 or 3 versions of
this course. In addition, the
students will complete two
units in an independent
study format.
Due to the accelerated
nature of this course, any
student needing serious and
ongoing remediation will be
advised to consider being
reassigned to the level 2
Algebra II course.
Otherwise, students will be
advised to stay after school
for extra help, utilize the
Mu Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Algebra II, Level 1
Page 35
Approx. Time Allotment:
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 35 -
November 2003
Essential Question, Concept or Theme: K. Matrices
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.I
Benchmark/Skills
Benchmark 1: Students will perform
basic mathematical operations
involving matrices.
Skill set
Perform scalar multiplication on a
matrix.
Add or subtract corresponding elements
of a matrix.
Determine whether two matrices can be
multiplied by verifying that the number
of columns in the first matrix is equal to
the number of rows in the second
matrix.
Multiply matrices by using the row by
column method.
Set corresponding elements of two
matrices equal to one another and solve
for any variables.
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Tests, quizzes, and a cumulative Algebra II - Integration,
final exam.
Applications & Connections Covered on a Midterm exam.
Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
Optional forms of assessment:
graphing calculators and
Homework, projects, teacher
overhead view screen.
observation in the classroom,
oral assessment, performance
Optional Resources:
assessment, group activities, or Teacher resource materials
board work.
associated with the text.
Computer software applications
for classroom demonstration or
individual student exploration.
Internet links suggested in the
text.
Videos available in the Penncrest
Math Office.
Boxer Math
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work independently of
the instructor and are permitted to
work with other students.
Optional instructional strategies
may include:
Group work, or any variety of
classroom activities such as “List,
Pass, Amass”, “Each one, teach
one”, etc. as suggested by the
Professional Development
Coordinator.
Independent investigations
Boxer Math Applications
Benchmark 2: Students will evaluate
the determinant of a 3 x 3 matrix.
Skill set
Evaluate the determinant first by the
method of expansion by minors.
Evaluate the determinant by using the
graphing calculator.
Benchmark 3: Students will
determine the area of a triangle given
the coordinates of its vertices.
Algebra II, Level 1
Page 36
- 36 -
November 2003
Essential Question, Concept or Theme: K. Matrices
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.I
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 4: Students will write the
identity matrix for any square matrix.
Benchmark 5: Students will
determine the inverse of a 2 x 2
matrix.
Benchmark 6: Students will solve
systems of linear equations by using
inverse and augmented matrices.
Optional Benchmark 7: Students will
be able to use a graphing calculator to
perform operations with matrices and
find determinants and inverses.
Algebra II, Level 1
Page 37
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November 2003
Essential Question, Concept or Theme: K. Matrices
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.I
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
By definition as a level 1
course, this course is an
enrichment course.
Students will be asked to
perform more difficult tests,
quizzes, and homework
assignments than those in
the level 2 or 3 versions of
this course. In addition, the
students will complete two
units in an independent
study format.
Due to the accelerated
nature of this course, any
student needing serious and
ongoing remediation will be
advised to consider being
reassigned to the level 2
Algebra II course.
Otherwise, students will be
advised to stay after school
for extra help, utilize the
Mu Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Algebra II, Level 1
Page 38
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 38 -
November 2003
Essential Question, Concept or Theme: L. Exponential and Logarithmic Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.N, 2.8.11.T, 2.11.11.A
Aligned Materials/
Resources/Technology
Benchmark/Skills
Assessment
Benchmark 1: Students will write
exponential equations in logarithmic
form and vice versa.
Skill set
m
Understand that a  n is equivalent to
loga n  m
Tests, quizzes, and a cumulative
final exam.
This unit is conducted as an
independent study unit for
accelerated students.
Assessments include 2 tests per
unit, and 7-8 written homework
assignments that are graded,
and a cumulative Final Exam.
Benchmark 2: Students will evaluate
logarithmic expressions.
Skill set
Evaluate simple expressions by
converting first to exponential form.
Evaluate expressions using the graphing
calculator.
Find common logarithms and
antilogarithms using the graphing
calculator.
Find natural logarithms of numbers
using the graphing calculator.
Approx. Time Allotment:
Optional forms of assessment:
Homework, projects, teacher
observation in the classroom,
oral assessment, performance
assessment, group activities, or
board work.
Algebra II - Integration,
Applications & Connections Glencoe/McGraw-Hill, 1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and
overhead view screen.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software applications
for classroom demonstration or
individual student exploration.
Internet links suggested in the
text.
Videos available in the Penncrest
Math Office.
Boxer Math
Instructional Strategies
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work independently of
the instructor and are permitted to
work with other students.
Optional instructional strategies
may include:
Group work, or any variety of
classroom activities such as “List,
Pass, Amass”, “Each one, teach
one”, etc. as suggested by the
Professional Development
Coordinator.
Independent investigations
Boxer Math Applications
Benchmark 3: Students will solve
equations and inequalities involving
logarithmic functions.
Skill set
Simplify and evaluate expressions using
properties of logarithms.
Solve equations with variable exponents
by using logarithms.
Algebra II, Level 1
Page 39
- 39 -
November 2003
Essential Question, Concept or Theme: L. Exponential and Logarithmic Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.N, 2.8.11.T, 2.11.11.A
Benchmark/Skills
Approx. Time Allotment:
Aligned Materials/
Resources/Technology
Assessment
Instructional Strategies
Benchmark 4: Students will use
logarithms to solve problems
involving growth and decay.
Benchmark 5: Students will identify
the characteristic and mantissa of a
logarithm.
Algebra II, Level 1
Page 40
- 40 -
November 2003
Essential Question, Concept or Theme: L. Exponential and Logarithmic Functions
PA Standards: 2.1.11.A, 2.2.11.F, 2.5.11.A-C, 2.8.11.N, 2.8.11.T, 2.11.11.A
Approx. Time Allotment:
Adaptations/Inclusion Techniques
Enrichment Strategies
Remediation Strategies
Adaptations for students with special instructional
needs will be met in accordance with each
student’s Individualized Educational Plan.
By definition as a level 1
course, this course is an
enrichment course.
Students will be asked to
perform more difficult tests,
quizzes, and homework
assignments than those in
the level 2 or 3 versions of
this course. In addition, the
students will complete two
units in an independent
study format.
Due to the accelerated
nature of this course, any
student needing serious and
ongoing remediation will be
advised to consider being
reassigned to the level 2
Algebra II course.
Otherwise, students will be
advised to stay after school
for extra help, utilize the
Mu Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Adaptations may include but are not limited to
extended time on tests and assignments,
preferential seating, after school help, or
modified homework assignments.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Algebra II, Level 1
Page 41
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 41 -
November 2003
Essential Question, Concept or Theme: M. Statistics
PA Standards: 2.6.11.A, 2.6.11.C, 2.6.11.D, 2.6.11.I
Benchmark/Skills
Benchmark 1: Students will be able to
represent and interpret data graphically.
Skill set
Students will create and interpret the following
types of graphs: line graph, circle graph, line plot,
stem and leaf plot, stem, leaf, back-to-back stem
and leaf plot
Benchmark 2: Find and use the mean, median
and mode to interpret data.
Skill set
Determine the mean, median, mode, measure of
central tendency, and extreme values for a data
set.
Approx. Time Allotment:
Assessment
Tests, quizzes, and a
cumulative final exam.
Optional forms of
assessment:
Homework, projects,
teacher observation in the
classroom, oral assessment,
performance assessment,
group activities, or board
work.
Benchmark 3: Students will model data with a
graph and linear equation.
Skill set
Draw scatter plots.
Find and use prediction equation.
Aligned Materials/
Resources/Technology
Instructional Strategies
Algebra II - Integration,
Applications &
Connections Glencoe/McGraw-Hill,
1998
TI-82, TI-83, or TI-83 Plus
graphing calculators and
overhead view screen.
Instructional strategies by the
teacher will include:
A.-M. Lecture, demonstration,
review, graphing calculator
activities.
L. Students work independently of
the instructor and are permitted to
work with other students.
Optional Resources:
Teacher resource materials
associated with the text.
Computer software
applications for classroom
demonstration or individual
student exploration.
Internet links suggested in
the text.
Videos available in the
Penncrest Math Office.
Boxer Math
Optional instructional strategies
may include:
Group work, or any variety of
classroom activities such as “List,
Pass, Amass”, “Each one, teach
one”, etc. as suggested by the
Professional Development
Coordinator.
Independent investigations
Boxer Math Applications
Benchmark 4: Students will use a graphing
calculator to graph lines of regression and to
graph linear inequalities.
Skill set
Basic understanding of the use of the graphing
calculator.
Benchmark 4: Students will determine the
standard deviation for a set of data.
Algebra II, Level 1
Page 42
- 42 -
November 2003
Essential Question, Concept or Theme: M. Statistics
PA Standards: 2.6.11.A, 2.6.11.C, 2.6.11.D, 2.6.11.I
Benchmark/Skills
Approx. Time Allotment:
Assessment
Aligned Materials/
Resources/Technology
Instructional Strategies
Benchmark 5: Students will solve problems
involving normally distributed data.
Benchmark 6: Students will use the binomial
expansion to find probabilities.
Benchmark 7: Students will use simulations to
solve various probability problems.
Skill set
Determine an unbiased sample.
Find margins of sampling error.
Test hypothesis by designing and conducting
experiments.
Algebra II, Level 1
Page 43
- 43 -
November 2003
Essential Question, Concept or Theme: M. Statistics
PA Standards: 2.6.11.A, 2.6.11.C, 2.6.11.D, 2.6.11.I
Adaptations/Inclusion Techniques
Approx. Time Allotment:
Enrichment Strategies
Adaptations for students with special instructional By definition as a level 1
needs will be met in accordance with each
course, this course is an
student’s Individualized Educational Plan.
enrichment course.
Students will be asked to
Adaptations may include but are not limited to
perform more difficult tests,
extended time on tests and assignments,
quizzes, and homework
preferential seating, after school help, or
assignments than those in
modified homework assignments.
the level 2 or 3 versions of
this course. In addition, the
students will complete two
units in an independent
study format.
Use enrichment workbook
associated with current
textbook to cover many
optional topics such as 4X4
determinants, probability
topics, etc.
Algebra II, Level 1
Page 44
Remediation Strategies
Due to the accelerated
nature of this course, any
student needing serious and
ongoing remediation will be
advised to consider being
reassigned to the level 2
Algebra II course.
Otherwise, students will be
advised to stay after school
for extra help, utilize the
Mu Alpha Theta tutoring
service offered at
Penncrest, or seek
professional tutoring
outside of the school day.
Multicultural/Interdisciplinary
Connection
The textbook contains many
applications that connect the math
topics to other fields of study.
Likewise, many of the applications
involve examples that are
multicultural in nature.
- 44 -
November 2003